Many are interested in understanding how the brain communicates at a systems level and how these systems are disrupted in neurological conditions and diseases. By modeling the brain as a network of functional brain connections, we seek to find network patterns that are altered in a group of patients or are associated with symptom severity. To achieve this, we introduce new two-level models using Gaussian Graphical Models to describe subject-level networks and Generalized Linear Models to describe population-level effects as a function of subject-level network patterns. This problem leads to a new statistical paradigm which we term Population Post Selection Inference (popPSI). To address this, we present a new estimation and inference technique, R^3, which employs resampling, random penalization, and random effects test statistics. Our method offers substantial improvements in statistical powerful and yields fewer false positives than existing approaches. We use our techniques to discover alterations in functional brain networks of patients with autism and neurofibromatosis.
Joint work with Manjari Narayan.